Monday, May 16, 2011

Why r-pentomino?

Okay, first a fair warning. I am a geek. I try not to be a nerd, but I am definitely an unrepentant geek. There you've been warned. that said...
r-pentomino is something I have adopted as a sort of personal symbol.

You See, there's this old math game, called 'The Game of Life'. In brief. It is a simple "game" played on a grid. First you fill in some cells on the grid. Then for each turn you evaluate the grid, based on a very small set of rules, to decide what the grid looks like on the next turn. Cells that are filled in are considered live, and cells that are empty are considered dead. each cell is evaluated using the following rules:

1. A live cell with less than two neighbors dies of loneliness.

2. A live cell with two or three neighbors stays alive.

3. A dead cell with exactly three neighbors becomes alive.

4. A live cell will more than three neighbors dies from overcrowding.

That's it. You then repeat the process until a stable state is reached (ie, one in which no changes occur, or the changes are a predictable pattern).

So, the r-pentomino is one pattern which you can place on the game of life board and play. Five cells in the simple arrangement shown above. This simple five cell arrangement, played in this simple game with it's very tiny set of rules, takes 1103 turns before it reaches a stable state! It isn't the only simple pattern which takes so long to stabilize either. But is is one which has been given a name (a cool sounding name at that).

Thus, the r-pentomino has become a personal symbol. A reminder to me that life is a very complicated thing with lots of rules and variables that all interrelate in fascinating ways. The r-pentomino reminds me that even seemingly simple aspects of life can be amazingly complicated, and may not turn out as I predict. It is my reminder to be patient with myself. My reminder that truth takes time to discover, and that what may appear to be the truth now, may look entirely different as I move back to see the bigger picture. It is my reminder to be persistent and forgiving.

So, there you have it. My goal with this blog is to reflect that. To share what little I have discovered of the pattern.